Anatomy of single-field inflationary models for primordial black holes

TL;DR

This paper introduces an analytically solvable model of single-field inflation that explains primordial black hole formation, consistent with observations, and explores how different scenarios affect the power spectrum and gravitational wave signals.

Contribution

It presents a simple, explicit inflationary model using Wands duality that captures PBH production and aligns with CMB data, providing a framework for various PBH masses.

Findings

The model can produce PBHs of arbitrary mass consistent with CMB observations.

Constraints exclude PBHs heavier than 10^4 solar masses in single-field inflation.

The shape of the curvature power spectrum peak varies across scenarios.

Abstract

We construct an analytically solvable simplified model that captures the essential features for primordial black hole (PBH) production in most models of single-field inflation. The construction makes use of the Wands duality between the constant-roll (or slow-roll) and the preceding ultra-slow-roll phases and can be realized by a simple inflaton potential of two joined parabolas. Within this framework, it is possible to formulate explicit inflationary scenarios consistent with the CMB observations and copious production of PBHs of arbitrary mass. We quantify the variability of the shape of the peak in the curvature power spectrum in different inflationary scenarios and discuss its implications for probing PBHs with scalar-induced gravitational wave backgrounds. We find that the COBE/Firas $\mu$-distortion constraints exclude the production of PBHs heavier than $10^4 M_\odot$ in single-field inflation.